The acquisition of fan-beam data using translate-rotate (TR) computed tomography (CT) (also often referred to as second generation) comprises a known area of endeavor. Using the resultant fan-beam data to form a corresponding image often involves the use of so-called sort-to-parallel algorithms. Though useful for at least some application settings, these sort-to-parallel algorithms do not meet the all requirements in all settings.
For example, many prior sorting algorithms typically require a resampling step in the channel and view directions and also typically require a resampling step in the view direction. These resampling steps are often done using interpolation (though, to be clear, resampling will be understood to refer to changing the set of locations where samples are effectively located and interpolation will be understood to refer to looking up (or synthesizing) the value of a datum at a location that does not exist). This in turn, can lead to loss of image quality due to the interpolations.
As another example, prior sorting algorithms typically require the rotation increment to either be equal to the fan angle or to match the known angular spacing between two arbitrary channels. This, in turn, imposes requirements upon rotation positions (for example, to avoid arbitrary fan overlap circumstances as may otherwise occur between successive translations). Such requirements can potentially impact image quality.
With at least some prior approaches the rotation increment must exactly match the fan angle (or an integer multiple of channel pitch or the like) if the geometry is accurately known ahead of time. As a result, if one guesses wrong when collecting the data and only later understands the geometry in better terms later, it will nevertheless be too late to use that information. Similarly, one cannot modify any determined geometry values that affect fan angle (source-to-detector distance or fan-angle itself being the prime candidates) after the fact to try and make the images better.
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